music.band_pass¶

music.band_pass(centre=0.1, bandwidth=0.05)[source]¶

A two-pole band pass, from the article’s eq:passa-banda.

With R and K from eq:varAux: a = [1 - K, 2(K - R)cos(2 pi f_c), R**2 - K] and b = [1, 2R cos(2 pi f_c), -R**2].

Parameters:

centrescalar: The centre of the band, as a fraction of the sample rate.
bandwidthscalar: The full width of the band between its 3 dB points, so they fall at centre +/- bandwidth / 2. The article’s prose says centre +/- bandwidth; its coefficients give half that, measured across every bandwidth tried. See DISCREPANCIES.md.

Returns:

a, bndarray: The feedforward and feedback coefficients, for iir().

Raises:

ValueError: If centre or bandwidth is outside (0, 0.5).

Parameters:

centre (float)
bandwidth (float)

Return type:

tuple[NDArray[float64], NDArray[float64]]

See also

band_reject: the same geometry, keeping what this one discards.

Notes

The article warns that these two filters amplify rather than attenuate when the centre is low and the band wide, and that at high centres they spread towards the bass rather than holding their shape. Neither is a defect in the coefficients; both are what a two-pole design does.

Examples

>>> a, b = band_pass(centre=0.1, bandwidth=0.02)
>>> len(a), len(b)
(3, 3)